Standard OFDM signals are formed as a weighted sum of orthogonal sampled data sine waves. Signals formed by this sum exhibit a large peak-to-average power ratio (“PAPR”). Having a large PAPR is generally undesirable as it leads to poor power efficiency in an amplifier. The 4-to-1 peak-to-average amplitude ratio is associated with a Rayleigh envelope which exhibits a large ratio of peak-to-average value with peak values generally exceeding approximately four times the average value with a probability of approximately 0.00035. In other words, to preserve fidelity of an OFDM time signal and to avoid spectral artifacts due to amplifier clipping, the amplifier may be operated with an average signal level at one-fourth of full scale. In other words, suppose for example that signals are to be passed with a 4-to-1 peak-to-average amplitude ratio through a power amplifier, such a peak power level would be 16 times the average power level. This means that an amplifier designed to deliver five watts of average power would have to be capable of delivering 80 watts of peak power. Furthermore, it should be understood that power amplifiers are generally inefficient in their transduction process of turning DC power into signal power when they are operating at small fractions of their peak power level.
Accordingly, it would be desirable and useful to reduce peak-to-average power levels of a transmitted signal. Along those lines, reductions in PAPR may result in significant reduction in power supply draw and waste heat used to deliver a specified average power.